L.A. County’s unemployment rate continued its rapid descent in March, falling to 5.4 percent, closing most of the unemployment gap with the rest of the nation.

The drop came as employer payrolls in the county showed a modest gain of nearly 13,000 jobs, state figures released Friday show.

The state Employment Development Department figures show the March unemployment rate for L.A. County shaved two-tenths of a percentage point off the February rate of 5.6 percent and was down two full percentage points from the rate of 7.4 percent a year ago. It also matched the statewide rate.

More importantly, the county now is no longer much worse off when it comes to unemployment than the rest of the nation. As the county rate has tumbled over the past year, the national rate has dipped only slightly to 5 percent from 5.4 percent. So the spread between the two has narrowed from two full percentage points a year ago to just four-tenths of a percentage point in March.

Even more remarkably, the unemployment rate in the city of Los Angeles was 5.3 percent in March, lower than the countywide average and only three-tenths of a percentage point above the national average. With pockets of poverty in Skid Row and large swaths of South Los Angeles, the city historically has seen unemployment rates up to three full percentage points above the national average; most of that difference is now gone.

This dramatic drop in unemployment means the local labor market is now the tightest it’s been in more than eight years. And that has shifted the playing field more in favor of workers.

“Employers are now having to be more competitive when it comes to filling job openings,” said Chris Garza, vice president for the greater Los Angeles region with Robert Half International, a Menlo Park staffing firm. “If they see a candidate they like, they have to pounce, because that candidate will likely have two or three other job offers in hand and will only take a day or two to decide.”

Turning to the net increase of 12,800 payroll jobs in March, the biggest gainer was local government, up 5,300 jobs. Other major gainers included accommodation/food services (up 3,100 jobs) and manufacturing (up 2,100).